New optical solitons of Tzitzeíca type evolution equations using extended trial approach

Abstract

The properties of Tzitzeica equations in nonlinear optics have been the discussion of many recent studies. In this article, a new and productive implementation of trial equation method is chosen to handle this class of nonlinear evolution equations. As a result, the new and more exact periodic, singular, hyperbolic and rational solutions of Tzitzeica, Dodd–Bullough–Mikhailov and Tzitzeica–Dodd–Bullough equations are formally obtained. The extended trial equation method along with the symbolic computation gives a versatile technique to deal such kinds of nonlinear evolution equations in nonlinear optics.